\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  19.0 & -4.00 x_{1} & +  8.00 x_{2} & +  5.00 x_{3} & -5.00 x_{4} & -7.00 x_{5} & -9.00 x_{6} & -5.00 x_{7} & +  3.00 x_{8} & -6.00 x_{9}\\
 x_{11}   &  34.0 & +  6.00 x_{1} & -10.00 x_{2} & -5.00 x_{3} & -10.00 x_{4} & -2.00 x_{5} & +  7.00 x_{6} & -10.00 x_{7} & -3.00 x_{8} & +  2.00 x_{9}\\
 x_{12}   &  25.0 & -10.00 x_{1} & -3.00 x_{2} &   & -5.00 x_{4} & +  7.00 x_{5} & +  2.00 x_{6} & +  8.00 x_{7} & +  6.00 x_{8} & -1.00 x_{9}\\
 x_{13}   &  51.0 & -10.00 x_{1} & +  5.00 x_{2} & +  1.00 x_{3} & -8.00 x_{4} & +  3.00 x_{5} & +  8.00 x_{6} & +  9.00 x_{7} & -1.00 x_{8} & -9.00 x_{9}\\
 x_{14}   &  9.0 & +  6.00 x_{1} & +  2.00 x_{2} & +  6.00 x_{3} & -8.00 x_{4} & +  2.00 x_{5} & +  4.00 x_{6} & +  8.00 x_{7} & -8.00 x_{8} & -8.00 x_{9}\\
\hline
z    &  0.0 & -3.00 x_{1} & +  1.00 x_{2} & -5.00 x_{3} & +  3.00 x_{4} &   & -4.00 x_{6} & -4.00 x_{7} & -1.00 x_{8} & -3.00 x_{9}\\
\end{array}\]
No initialization required --> Proceed to Optimize. 
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  19.0 & -4.00 x_{1} & +  8.00 x_{2} & +  5.00 x_{3} & -5.00 x_{4} & -7.00 x_{5} & -9.00 x_{6} & -5.00 x_{7} & +  3.00 x_{8} & -6.00 x_{9}\\
 x_{11}   &  34.0 & +  6.00 x_{1} & -10.00 x_{2} & -5.00 x_{3} & -10.00 x_{4} & -2.00 x_{5} & +  7.00 x_{6} & -10.00 x_{7} & -3.00 x_{8} & +  2.00 x_{9}\\
 x_{12}   &  25.0 & -10.00 x_{1} & -3.00 x_{2} &   & -5.00 x_{4} & +  7.00 x_{5} & +  2.00 x_{6} & +  8.00 x_{7} & +  6.00 x_{8} & -1.00 x_{9}\\
 x_{13}   &  51.0 & -10.00 x_{1} & +  5.00 x_{2} & +  1.00 x_{3} & -8.00 x_{4} & +  3.00 x_{5} & +  8.00 x_{6} & +  9.00 x_{7} & -1.00 x_{8} & -9.00 x_{9}\\
 x_{14}   &  9.0 & +  6.00 x_{1} & +  2.00 x_{2} & +  6.00 x_{3} & -8.00 x_{4} & +  2.00 x_{5} & +  4.00 x_{6} & +  8.00 x_{7} & -8.00 x_{8} & -8.00 x_{9}\\
\hline
z    &  0.0 & -3.00 x_{1} & +  1.00 x_{2} & -5.00 x_{3} & +  3.00 x_{4} &   & -4.00 x_{6} & -4.00 x_{7} & -1.00 x_{8} & -3.00 x_{9}\\
\end{array}\]


 $ x_{2} $ enters and $ x_{11} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  46.2 & +  0.80 x_{1} & -0.80 x_{11} & +  1.00 x_{3} & -13.00 x_{4} & -8.60 x_{5} & -3.40 x_{6} & -13.00 x_{7} & +  0.60 x_{8} & -4.40 x_{9}\\
 x_{2}   &  3.4 & +  0.60 x_{1} & -0.10 x_{11} & -0.50 x_{3} & -1.00 x_{4} & -0.20 x_{5} & +  0.70 x_{6} & -1.00 x_{7} & -0.30 x_{8} & +  0.20 x_{9}\\
 x_{12}   &  14.8 & -11.80 x_{1} & +  0.30 x_{11} & +  1.50 x_{3} & -2.00 x_{4} & +  7.60 x_{5} & -0.10 x_{6} & + 11.00 x_{7} & +  6.90 x_{8} & -1.60 x_{9}\\
 x_{13}   &  68.0 & -7.00 x_{1} & -0.50 x_{11} & -1.50 x_{3} & -13.00 x_{4} & +  2.00 x_{5} & + 11.50 x_{6} & +  4.00 x_{7} & -2.50 x_{8} & -8.00 x_{9}\\
 x_{14}   &  15.8 & +  7.20 x_{1} & -0.20 x_{11} & +  5.00 x_{3} & -10.00 x_{4} & +  1.60 x_{5} & +  5.40 x_{6} & +  6.00 x_{7} & -8.60 x_{8} & -7.60 x_{9}\\
\hline
z    &  3.4 & -2.40 x_{1} & -0.10 x_{11} & -5.50 x_{3} & +  2.00 x_{4} & -0.20 x_{5} & -3.30 x_{6} & -5.00 x_{7} & -1.30 x_{8} & -2.80 x_{9}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{14} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  25.66 & -8.56 x_{1} & -0.54 x_{11} & -5.50 x_{3} & +  1.30 x_{14} & -10.68 x_{5} & -10.42 x_{6} & -20.80 x_{7} & + 11.78 x_{8} & +  5.48 x_{9}\\
 x_{2}   &  1.82 & -0.12 x_{1} & -0.08 x_{11} & -1.00 x_{3} & +  0.10 x_{14} & -0.36 x_{5} & +  0.16 x_{6} & -1.60 x_{7} & +  0.56 x_{8} & +  0.96 x_{9}\\
 x_{12}   &  11.64 & -13.24 x_{1} & +  0.34 x_{11} & +  0.50 x_{3} & +  0.20 x_{14} & +  7.28 x_{5} & -1.18 x_{6} & +  9.80 x_{7} & +  8.62 x_{8} & -0.08 x_{9}\\
 x_{13}   &  47.46 & -16.36 x_{1} & -0.24 x_{11} & -8.00 x_{3} & +  1.30 x_{14} & -0.08 x_{5} & +  4.48 x_{6} & -3.80 x_{7} & +  8.68 x_{8} & +  1.88 x_{9}\\
 x_{4}   &  1.58 & +  0.72 x_{1} & -0.02 x_{11} & +  0.50 x_{3} & -0.10 x_{14} & +  0.16 x_{5} & +  0.54 x_{6} & +  0.60 x_{7} & -0.86 x_{8} & -0.76 x_{9}\\
\hline
z    &  6.56 & -0.96 x_{1} & -0.14 x_{11} & -4.50 x_{3} & -0.20 x_{14} & +  0.12 x_{5} & -2.22 x_{6} & -3.80 x_{7} & -3.02 x_{8} & -4.32 x_{9}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{5}   &  2.40262172285 & -0.80 x_{1} & -0.05 x_{11} & -0.51 x_{3} & +  0.12 x_{14} & -0.09 x_{10} & -0.98 x_{6} & -1.95 x_{7} & +  1.10 x_{8} & +  0.51 x_{9}\\
 x_{2}   &  0.955056179775 & +  0.17 x_{1} & -0.06 x_{11} & -0.81 x_{3} & +  0.06 x_{14} & +  0.03 x_{10} & +  0.51 x_{6} & -0.90 x_{7} & +  0.16 x_{8} & +  0.78 x_{9}\\
 x_{12}   &  29.1310861423 & -19.07 x_{1} & -0.03 x_{11} & -3.25 x_{3} & +  1.09 x_{14} & -0.68 x_{10} & -8.28 x_{6} & -4.38 x_{7} & + 16.65 x_{8} & +  3.66 x_{9}\\
 x_{13}   &  47.2677902622 & -16.30 x_{1} & -0.24 x_{11} & -7.96 x_{3} & +  1.29 x_{14} & +  0.01 x_{10} & +  4.56 x_{6} & -3.64 x_{7} & +  8.59 x_{8} & +  1.84 x_{9}\\
 x_{4}   &  1.96441947566 & +  0.59 x_{1} & -0.03 x_{11} & +  0.42 x_{3} & -0.08 x_{14} & -0.01 x_{10} & +  0.38 x_{6} & +  0.29 x_{7} & -0.68 x_{8} & -0.68 x_{9}\\
\hline
z    &  6.84831460674 & -1.06 x_{1} & -0.15 x_{11} & -4.56 x_{3} & -0.19 x_{14} & -0.01 x_{10} & -2.34 x_{6} & -4.03 x_{7} & -2.89 x_{8} & -4.26 x_{9}\\
\end{array}\]
Final Dictionary
Solution:  6.84831460674
Num Pivots:  4
\end{document}
